Quantum Physics and Mathematical Debates Concerning the Problem of the Ontological Priority between Continuous Quantity and Discrete Quantity

Abstract

In his book about the Categories (that is about the ultimate elements of classification and order), in the chapter concerning the quantity (IV, 20) Aristotle says that this concept recovers two kinds of modalities: the discrete quantity and the continuous quantity and he gives as examples the number for the first one; line, surface, solid, times and space for the second one. The main philosophical problem raised by this text is to determine which of the two modalities of the quantity has the ontological priority over the other (given two concepts A and B, we assume that A has ontological priority over B if every entity that possesses the quality B possesses necessarily the quality A). The problem is magnified by the fact that space, which in some part of Aristotle’s Physics is mentioned not only as a category properly speaking but even as the main category whose power can be amazing, is in the evoked text of the Categories’s Book reduced to expression of the continuum, and sharing this condition with time. In this matter the controversy is constant through the common history of Science and Philosophy.

In this paper we will recall the main points of projection of the controversy through the history of thought, from Zeno’s aporias (and the mathematical attempts of solution) to the contemporary non standard analysis. To summarize: in order to display the ontological weight of quantum physics we will replace in its philosophical background the dramatic moment when Einstein suggested that Max Planck’s theory was faraway of being merely an speculative mathematical construction, and that energy in nature actually comes in indivisible packets, instead of infinitely divisible streams. We will ask ourselves what different answers to the question have been brought forward by the ulterior developments of the discipline. In a second part of the paper we will try to establish the link between the problem raised up, the controversies about quantum non locality and the contemporary philosophical objections concerning the lack of rational explanation in the quantum theory, in spite of being largely successful at predicting the results of atomic processes. For, as the Newton’s hypothesis non fingo displays, description and prevision does not necessarily means explanation.